Problem: $a_n=\dfrac{\ln(n)}{5^n}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Explanation: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}}\, \right|=\dfrac{1}{5}$ Since the limit, $\dfrac{1}{5}$, is less than $1$, the ratio test tells us that the series converges.